Topological quantum codes from self-complementary self-dual graphs

TL;DR

This paper introduces two new classes of binary quantum codes derived from self-complementary self-dual graphs, achieving high code rates and minimum distance of at least three, expanding quantum error correction capabilities.

Contribution

It presents novel quantum codes based on self-complementary self-dual embeddings of voltage and Paley graphs, with parameters approaching optimal code rates.

Findings

Code rate approaches 1 as k increases

Minimum distance of at least 3 for all codes

New classes of quantum codes from graph embeddings

Abstract

In this paper we present two new classes of binary quantum codes with minimum distance of at least three, by self-complementary self-dual orientable embeddings of voltage graphs and Paley graphs in the Galois field GF(pr), where p is a prime number and r is a positive integer. The parameters of two new classes of quantum codes are [[(2k+2)(8k+ 7); 2(8k^2+7k); d]] and [[(2k+2)(8k+9); 2(8k^2+9k+1); d]] respectively, where d>=3. For these quantum codes, the code rate approaches 1 as k goes to infinity.